This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

There is intense interest in graphene in fields such as physics, chemistry, and materials science, among others. Interest in graphene's exceptional physical properties, chemical tunability, and potential for applications has generated thousands of publications and an accelerating pace of research, making review of such research timely. Here is an overview of the synthesis, properties, and applications of graphene and related materials (primarily, graphite oxide and its colloidal suspensions and materials made from them), from a materials science perspective.

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Graphene and Graphene Oxide: Synthesis, Properties, and Applications

Every few years, a new material with unique properties emerges and fascinates the scientific community, typical recent examples being high-temperature superconductors and carbon nanotubes. Graphene is the latest sensation with unusual properties, such as half-integer quantum Hall effect and ballistic electron transport. This two-dimensional material which is the parent of all graphitic carbon forms is strictly expected to comprise a single layer, but there is considerable interest in investigating two-layer and few-layer graphenes as well. Synthesis and characterization of graphenes pose challenges, but there has been considerable progress in the last year or so. Herein, we present the status of graphene research which includes aspects related to synthesis, characterization, structure, and properties.

Graphene: The New Two-Dimensional Nanomaterial

Graphene, or single-layered graphite, with its high crystallinity and interesting semimetal electronic properties, has emerged as an exciting two-dimensional material showing great promise for the fabrication of nanoscale devices. Thin, elongated strips of graphene that possess straight edges, termed graphene ribbons, gradually transform from semiconductors to semimetals as their width increases, and represent a particularly versatile variety of graphene. Several lithographic, chemical and synthetic procedures are known to produce microscopic samples of graphene nanoribbons, and one chemical vapour deposition process has successfully produced macroscopic quantities of nanoribbons at 950 degrees C. Here we describe a simple solution-based oxidative process for producing a nearly 100% yield of nanoribbon structures by lengthwise cutting and unravelling of multiwalled carbon nanotube (MWCNT) side walls. Although oxidative shortening of MWCNTs has previously been achieved, lengthwise cutting is hitherto unreported. Ribbon structures with high water solubility are obtained. Subsequent chemical reduction of the nanoribbons from MWCNTs results in restoration of electrical conductivity. These early results affording nanoribbons could eventually lead to applications in fields of electronics and composite materials where bulk quantities of nanoribbons are required.

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Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons

Graphene based materials: Past, present and future

We have fabricated graphene nano-ribbon field-effect transistor devices and investigated their electrical properties as a function of ribbon width. Our experiments show that the resistivity of a ribbon increases as its width decreases, indicating the impact of edge states. Analysis of temperature-dependent measurements suggests a finite quantum confinement gap opening in narrow ribbons. The electrical current noise of the graphene ribbon devices at low frequency is found to be dominated by the 1/f noise.

Graphene nano-ribbon electronics

Silicon p(+)-i-n(+) diode Mach-Zehnder electrooptic modulators having an ultra-compact length of 100 to 200 mum are presented. These devices exhibit high modulation efficiency, with a V(pi)L figure of merit of 0.36 V-mm. Optical modulation at data rates up to 10 Gb/s is demonstrated with low RF power consumption of only 5 pJ/bit.

Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator.

Phase-change storage is widely used in optical information technologies (DVD, CD-ROM and so on), and recently it has also been considered for non-volatile memory applications. This work reports advances in thermal data recording of phase-change materials. Specifically, we show erasable thermal phase-change recording at a storage density of 3.3 Tb inch(-2), which is three orders of magnitude denser than that currently achievable with commercial optical storage technologies. We demonstrate the concept of a thin-film nanoheater to realize ultra-small heat spots with dimensions of less than 50 nm. Finally, we show in a proof-of-concept demonstration that an individual thin-film heater can write, erase and read the phase of these storage materials at competitive speeds. This work provides important stepping stones for a very-high-density storage or memory technology based on phase-change materials.

Ultra-high-density phase-change storage and memory.

We report the first direct capacitance measurements of silicon nanowires (SiNWs) and the consequent determination of field carrier mobilities in undoped-channel SiNW field-effect transistors (FETs) at room temperature. We employ a two-FET method for accurate extraction of the intrinsic channel resistance and intrinsic channel capacitance of the SiNWs. The devices used in this study were fabricated using a top-down method to create SiNW FETs with up to 1000 wires in parallel for increasing the raw capacitance while maintaining excellent control on device dimensions and series resistance. We found that, compared with the universal mobility curves for bulk silicon, the electron and hole mobilities in nanowires are comparable to those of the surface orientation that offers a lower mobility.

Measurement of Carrier Mobility in Silicon Nanowires

The statistical distribution of random telegraph noise (RTN) has been measured and characterized in scaled PDSOI FETs down to 20nm gate length. Statistical analysis of RTN in ≫ 15 thousand nFETs shows temperature-independent long-tailed non-Gaussian distributions of noise amplitudes. Treated as equivalent threshold voltage variation (ΔV th ), the RTN distributions appear log-normal, with the ΔV th reaching ≫ 70 mV for the smalles devices. Because of the log-normal distribution, it appears that RTN V th variations may exceed random dopant fluctuation (RDF) V th variations at the ∼3 sigma level in the 22 nm generation, making RTN a very serious threat to SRAM stability at 22 nm and beyond.

Michael J. Rooks

Papers

Graphene nano-ribbon electronics

Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator.

Ultra-high-density phase-change storage and memory.

Measurement of Carrier Mobility in Silicon Nanowires

Increasing threshold voltage variation due to random telegraph noise in FETs as gate lengths scale to 20 nm